Various approaches have been proposed for quantum computing. Perhaps the most familiar of these is the quantum circuit model (QCM). The challenge in QCM is to identify a suitable subset of a universal set of quantum gates that can faithfully represent a family of unitary operations on d qubits (d-partite), such that the number of gates required scale polynomially in d, whilst the dimension grows exponentially as 2d. After the unitary evolution, the output needs to be projected onto the computational basis and irreversibly measured. One realization of the QCM has been linear optical quantum computing (LOQC) and one-way quantum computing (OWQC), which are also known as cluster-state quantum computing. The essential feature of each of these approaches involves either a non-linear measuring process, a preparation of hyper-entangled input states (|IN), or both. Here a sequence of measurements are made to project the output state (|OUT) onto one or another of the computational basis states, i.e. onto a mutually unbiased basis (MUB).
In practice, it has been suggested that photons offer great promise for producing gates according to the QCM model for quantum information processing (QIP) given their robustness to decoherence. However, it is this very resiliency that hinders their utility in quantum computing. In particular, their weak coupling with atomic structures leads to substantial inefficiencies. Further, practical implementations of photonic gates are typically complex and their stability is often at issue.